This project is intended to increase our understanding of the use and application of models in toxicology and biochemistry and to implement new mathematical models to aid in explaining current research findings. The research effort explores a diverse range of biological areas including carcinogenesis, pharmacology, developmental biology and immunology. In carcinogenesis, the adequacy of the multistage model of carcinogenesis for estimating tumor incidence rates in untreated animals was evaluated. Also, an estimate of carcinogenic potency from animal experiments which adjusts for chemically related changes in survival has been developed and is being evaluated. A mathematical model of carcinogenesis which explicitly incorporates DNA repair into the multistage process is under development. The mathematical details allowing us to use the model have been developed and current research is focused on using data for implementing this model for example chemicals. In another research area, the design of animal experiments, the implications of a clonal two-stage model of carcinogenesis on the design of the two-year rodent bioassay was evaluated. A simple design using age-dependent dosing schemes produced unique patterns of tumor incidence which can provide better information on carcinogenic mechanism. This research is continuing with emphasis on the number of stages in the carcinogenesis process. We are also studying the shape of carcinogenesis dose-response curves using information on biological activity of the chemical . Choosing the proper shape (threshold or not) is critical to an accurate estimate of carcinogenic risk. In teratology, several risk assessment models were evaluated for agreement with existing data. No model was found to be adequate and some were found to produce misleading results. Another effort in teratology concerns the ability of resampling techniques and quasi-likelihood methods to account for interlitter correlations. Additional research into the estimation of risks of mortality and morbidity from exposure to immunosuppressive chemicals has begun.